The New York Times reported last week that the district attorney in Los Angeles had recently reopened an investigation into the December 2000 killing of Durst's friend Susan Berman, and was tying it to the case of Kathleen Durst, who went missing from New York and was eventually pronounced legally dead.

In a telephone interview with the newspaper, Durst said he did not have the "faintest idea" who killed Berman, nor did he know what happened to his first wife, it reported.

In a separate case, after being arrested while living in Texas disguised as a mute woman, Durst was acquitted of murder in 2001 after convincing a jury that he had fatally shot and dismembered an elderly neighbor in an act of self-defense.

But in the final installment of a six-part HBO documentary series called "The Jinx: The Life and Deaths of Robert Durst" aired on Sunday night, Durst appears to say he carried out the killings.

Former Wife: Durst is pictured here with his first Kathleen wife, who disappeared in 1982

However it is not known if he is speaking sincerely, as was captured speaking to himself.

The documentary shows an interview session during which he rejects one piece of evidence against him.

Durst then goes to the bathroom still wearing the microphone and apparently unaware he is still being taped.

In remarks captured on audiotape in the bathroom, but not filmed, he whispers to himself: "What the hell did I do? Killed them all, of course."

Wealthy Family: Durst's family are responsible for many of New Yorks largest skyscrapers (Image: Getty)

In December 2014, Durst appeared in a New York courtroom on charges of trespassing on property owned by his estranged family.

The Durst Organization oversees the lease and maintenance of One World Trade Center, the western world's tallest skyscraper, built on the site of the destroyed twin towers in New York.

It is also responsible for a good portion of the city's skyline - the company says it owns 11 Manhattan office towers.